(Old) SFARI Genes
# !diagnostics off
library(tidyverse) ; library(reshape2) ; library(glue) ; library(plotly) ; library(plotlyutils)
library(RColorBrewer) ; library(viridis) ; require(gridExtra) ; library(GGally) ; library(ggpubr)
library(Rtsne)
library(ClusterR)
library(DESeq2)
library(expss)
library(knitr) ; library(kableExtra)Load preprocessed dataset (preprocessing code in 01_data_preprocessing.Rmd)
# Gandal dataset
load('./../Data/preprocessed_data.RData')
datExpr = datExpr %>% data.frame
genes_info = DE_info %>% data.frame
# GO Neuronal annotations: regex 'neuron' in GO functional annotations and label the genes that make a match as neuronal
GO_annotations = read.csv('./../Data/genes_GO_annotations.csv')
GO_neuronal = GO_annotations %>% filter(grepl('neuron', go_term)) %>%
mutate('ID'=as.character(ensembl_gene_id)) %>%
dplyr::select(-ensembl_gene_id) %>% distinct(ID) %>%
mutate('Neuronal'=1)
# SFARI Genes
SFARI_genes = read_csv('./../../../SFARI/Data/SFARI_genes_08-29-2019_w_ensembl_IDs.csv')
SFARI_genes = SFARI_genes[!duplicated(SFARI_genes$ID) & !is.na(SFARI_genes$ID),]
# Update DE_info with SFARI and Neuronal information
genes_info = genes_info %>% mutate('ID'=rownames(.)) %>% left_join(SFARI_genes, by='ID') %>%
mutate(`gene-score`=ifelse(is.na(`gene-score`), 'Others', `gene-score`)) %>%
distinct(ID, .keep_all = TRUE) %>% left_join(GO_neuronal, by='ID') %>%
mutate(Neuronal=ifelse(is.na(Neuronal), 0, Neuronal)) %>%
mutate(gene.score=ifelse(`gene-score`=='Others' & Neuronal==1, 'Neuronal', `gene-score`),
significant=padj<0.05 & !is.na(padj)) %>%
mutate(Group = factor(ifelse(gene.score %in% c('Neuronal','Others'), gene.score, 'SFARI'),
levels = c('SFARI', 'Neuronal', 'Others')))
SFARI_colour_hue = function(r) {
pal = c('#FF7631','#FFB100','#E8E328','#8CC83F','#62CCA6','#59B9C9','#b3b3b3','#808080','gray','#d9d9d9')[r]
}
rm(GO_annotations)SFARI Gene list
There are 980 genes with a SFARI score, but to map them to the gene expression dataset we had to map the gene names to their corresponding ensembl IDs
Mapping SFARI Gene names to Ensembl IDs
There are 1180 Ensembl IDs corresponding to the 980 genes in the SFARI Gene dataset
Since a gene can have more than one ensembl ID, there were some one-to-many mappings between a gene name and ensembl IDs, so that’s why we ended up with 1180 rows in the SFARI_genes dataset.
The details about how the genes were annotated with their Ensembl IDs can be found in SecondYear/SFARI/RMarkdowns/get_ensembl_ids_new_SFARI.html
There are 24 genes in the SFARI list without a score, of which 3 don’t have syndromic tag either
Exploratory Analysis
There are 924 SFARI Genes in the expression dataset (~78%)
Of these, only 902 have an assigned score
From now on, we’re only going to focus on these 902 genes with a score
Gene count by SFARI score:
table_info = genes_info %>% apply_labels(`gene-score` = 'SFARI Gene Score', syndromic = 'Syndromic Tag',
Neuronal = 'Neuronal Function', gene.score = 'Gene Score') %>%
mutate(syndromic = as.logical(syndromic), Neuronal = as.logical(Neuronal))
cro(table_info$`gene-score`)| #Total | |
|---|---|
| SFARI Gene Score | |
| 1 | 25 |
| 2 | 65 |
| 3 | 191 |
| 4 | 433 |
| 5 | 165 |
| 6 | 23 |
| Others | 15230 |
| #Total cases | 16132 |
Gene count by Syndromic tag:
cro(table_info$syndromic)| #Total | |
|---|---|
| Syndromic Tag | |
| FALSE | 816 |
| TRUE | 108 |
| #Total cases | 924 |
GO Neuronal annotations:
1094 genes have neuronal-related annotations
182 of these genes have a SFARI score
cro(table_info$gene.score[genes_info$`gene-score` %in% as.character(c(1:6))],
list(table_info$Neuronal[genes_info$`gene-score` %in% as.character(c(1:6))], total()))| Neuronal Function | #Total | |||
|---|---|---|---|---|
| FALSE | TRUE | |||
| Gene Score | ||||
| 1 | 16 | 9 | 25 | |
| 2 | 48 | 17 | 65 | |
| 3 | 149 | 42 | 191 | |
| 4 | 359 | 74 | 433 | |
| 5 | 129 | 36 | 165 | |
| 6 | 19 | 4 | 23 | |
| #Total cases | 720 | 182 | 902 | |
rm(table_info)
All SFARI scores together
Gene Expression
Larger mean expression than the other two groups, smaller SD than Neuronal genes
Note: SD plot was truncated so not all outliers are included
plot_data = data.frame('ID'=rownames(datExpr), 'MeanExpr'=rowMeans(datExpr), 'SDExpr'=apply(datExpr,1,sd)) %>%
left_join(genes_info, by='ID') %>%
mutate(Group = factor(ifelse(gene.score %in% c('Neuronal','Others'), gene.score, 'SFARI'),
levels = c('SFARI', 'Neuronal', 'Others')))
comparisons = list(c('SFARI','Neuronal'), c('Neuronal','Others'), c('SFARI','Others'))
increase = 1
base = 14.5
pos_y_comparisons = c(1:3*increase + base)
p1 = plot_data %>% ggplot(aes(Group, MeanExpr, fill=Group)) +
geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) +
stat_compare_means(comparisons = comparisons, label = 'p.signif', method = 't.test',
method.args = list(var.equal = FALSE), label.y = pos_y_comparisons, tip.length = .02) +
scale_fill_manual(values=c('#00A4F7', SFARI_colour_hue(r=c(8,7)))) +
xlab('') + ylab('Mean Expression') + ggtitle('Mean Expression Comparison') +
theme_minimal() + theme(legend.position='none')
increase = 0.03
base = 0.35
pos_y_comparisons = c(1:3*increase + base)
p2 = plot_data %>% ggplot(aes(Group, SDExpr, fill=Group)) +
geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) +
stat_compare_means(comparisons = comparisons, label = 'p.signif', method = 't.test',
method.args = list(var.equal = FALSE), label.y = pos_y_comparisons, tip.length = .01) +
scale_fill_manual(values=c('#00A4F7', SFARI_colour_hue(r=c(8,7)))) +
coord_cartesian(ylim= c(0.05, max(pos_y_comparisons))) +
xlab('') + ylab('Standard Deviation') + ggtitle('Standard Deviation Comparison') +
theme_minimal() + theme(legend.position='none')
grid.arrange(p1, p2, nrow=1)
rm(p1, p2, increase, base, pos_y_comparisons)Log Fold Change
Proportion of over- and under-expressed genes is very similar between groups: approximately half
genes_info %>% mutate(direction = ifelse(log2FoldChange>0, 'over-expressed', 'under-expressed')) %>%
group_by(Group, direction) %>% tally(name = 'over_expressed') %>%
filter(direction == 'over-expressed') %>% ungroup %>%
left_join(genes_info %>% group_by(Group) %>% tally(name = 'Total'), by = 'Group') %>% ungroup %>%
mutate('prop_over_expressed' = round(over_expressed/Total,3)) %>%
dplyr::select(-direction) %>% kable %>% kable_styling(full_width = F)| Group | over_expressed | Total | prop_over_expressed |
|---|---|---|---|
| SFARI | 438 | 902 | 0.486 |
| Neuronal | 447 | 912 | 0.490 |
| Others | 7370 | 14318 | 0.515 |
Smaller LFC magnitude than Neuronal genes and similar but slightly lower than the rest of the genes. The differences are statistically significant in all cases
increase = 0.04
base = 0.4
pos_y_comparisons = c(1:3*increase + base)
plot_data %>% ggplot(aes(Group, abs(log2FoldChange), fill=Group)) +
geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) +
stat_compare_means(comparisons = comparisons, label = 'p.signif', method = 't.test',
method.args = list(var.equal = FALSE), label.y = pos_y_comparisons,
tip.length = .005) +
scale_fill_manual(values=c('#00A4F7', SFARI_colour_hue(r=c(8,7)))) +
coord_cartesian(ylim= c(0.05, max(pos_y_comparisons))) +
xlab('') + ylab('LFC Magnitude') + ggtitle('LFC Magnitude Comparison') +
theme_minimal() + theme(legend.position='none')
rm(increase, base, pos_y_comparisons)- SFARI Genes, as a group, have less genes with high (positive) LFC than the rest of the genes in the dataset
plot_data = genes_info %>% dplyr::select(Group, log2FoldChange) %>%
mutate(quant = cut(log2FoldChange, breaks = quantile(log2FoldChange, probs = seq(0,1,0.05)) %>%
as.vector, labels = FALSE),
value_range = cut(log2FoldChange, breaks = quantile(log2FoldChange, probs=seq(0,1,0.05)) %>%
as.vector)) %>%
filter(Group == 'SFARI') %>% group_by(quant, value_range) %>% tally %>% ungroup %>%
left_join(genes_info %>% dplyr::select(Group, log2FoldChange) %>%
mutate(quant = cut(log2FoldChange, breaks = quantile(log2FoldChange,
probs = seq(0,1,0.05)) %>% as.vector, labels = FALSE)) %>%
group_by(quant) %>% tally(name = 'tot') %>% ungroup) %>% mutate(p = 100*n/tot)
ggplotly(plot_data %>% ggplot(aes(quant, p)) + geom_smooth(color = 'gray', alpha = 0.1) +
geom_bar(stat = 'identity', fill = '#00A4F7', aes(id = value_range)) +
geom_hline(yintercept = 100*mean(genes_info$Group == 'SFARI'), color = 'gray', linetype = 'dotted') +
xlab('Log Fold Change Quantiles') + ylab('% of SFARI Genes in each Quantile') + ggtitle('
Distribution of SFARI Genes in LFC Quantiles') + theme_minimal())data.frame('Quantile' = 1:20, 'LFC Range' = cut(genes_info$log2FoldChange,
breaks = quantile(genes_info$log2FoldChange, probs=seq(0,1,.05)) %>% as.vector) %>% table %>% names) %>%
kable(caption = 'LFC ranges for each quantile') %>% kable_styling(full_width = F)| Quantile | LFC.Range |
|---|---|
| 1 | (-2.03,-0.228] |
| 2 | (-0.228,-0.164] |
| 3 | (-0.164,-0.125] |
| 4 | (-0.125,-0.0985] |
| 5 | (-0.0985,-0.0778] |
| 6 | (-0.0778,-0.0597] |
| 7 | (-0.0597,-0.0425] |
| 8 | (-0.0425,-0.0259] |
| 9 | (-0.0259,-0.0113] |
| 10 | (-0.0113,0.00366] |
| 11 | (0.00366,0.0189] |
| 12 | (0.0189,0.0353] |
| 13 | (0.0353,0.052] |
| 14 | (0.052,0.073] |
| 15 | (0.073,0.097] |
| 16 | (0.097,0.129] |
| 17 | (0.129,0.17] |
| 18 | (0.17,0.238] |
| 19 | (0.238,0.373] |
| 20 | (0.373,1.96] |
Differential Expression
Lower proportion of DE genes than genes with Neuronal annotation but higher than the rest of the genes
genes_info %>% group_by(Group, significant) %>% tally(name = 'DE') %>% filter(significant) %>% ungroup %>%
left_join(genes_info %>% group_by(Group) %>% tally(name = 'Total'), by = 'Group') %>% ungroup %>%
mutate('prop_DE' = round(DE/Total,2)) %>% dplyr::select(-significant) %>%
kable(caption = 'Proportion of DE Genes by Group') %>% kable_styling(full_width = F)| Group | DE | Total | prop_DE |
|---|---|---|---|
| SFARI | 272 | 902 | 0.30 |
| Neuronal | 336 | 912 | 0.37 |
| Others | 3883 | 14318 | 0.27 |
SFARI Genes have consistently a lower percentage of DE genes than the Genes with Neuronal annotations and a slightly hiher level to the rest of the genes
lfc_list = seq(1, 1.2, 0.01)
all_counts = data.frame('group'='All', 'n'=as.character(nrow(genes_info)))
Others_counts = data.frame('group'='Others', n=as.character(sum(genes_info$Group == 'Others')))
Neuronal_counts = data.frame('group'='Neuronal', n=as.character(sum(genes_info$Neuronal)))
lfc_counts_all = genes_info %>% filter(Group == 'SFARI') %>% tally %>%
mutate('group'='SFARI', 'n'=as.character(n)) %>%
dplyr::select(group, n) %>%
bind_rows(Neuronal_counts, Others_counts, all_counts) %>%
mutate('lfc'=-1) %>% dplyr::select(lfc, group, n)
for(lfc in lfc_list){
# Recalculate genes_info with the new threshold (p-values change)
DE_genes = results(dds, lfcThreshold=log2(lfc), altHypothesis='greaterAbs') %>% data.frame %>%
mutate('ID' = rownames(.)) %>%
left_join(genes_info %>% dplyr::select(ID, Neuronal, gene.score, Group), by = 'ID') %>%
filter(padj<0.05 & abs(log2FoldChange)>log2(lfc))
# Calculate counts by groups
all_counts = data.frame('group'='All', 'n'=as.character(nrow(DE_genes)))
Others_counts = data.frame('group'='Others', n=as.character(sum(DE_genes$Group == 'Others')))
Neuronal_counts = data.frame('group'='Neuronal', n=as.character(sum(DE_genes$Neuronal)))
lfc_counts = DE_genes %>% filter(Group == 'SFARI') %>% tally %>%
mutate('group'='SFARI', 'n'=as.character(n)) %>%
bind_rows(Neuronal_counts, Others_counts, all_counts) %>%
mutate('lfc'=lfc) %>% dplyr::select(lfc, group, n)
# Update lfc_counts_all
lfc_counts_all = lfc_counts_all %>% bind_rows(lfc_counts)
}
# Add missing entries with 0s
lfc_counts_all = expand.grid('group'=unique(lfc_counts_all$group), 'lfc'=unique(lfc_counts_all$lfc)) %>%
left_join(lfc_counts_all, by=c('group','lfc')) %>% replace(is.na(.), 0)
# Calculate percentage of each group remaining
tot_counts = genes_info %>% filter(Group == 'SFARI') %>% tally() %>%
mutate('group'='SFARI', 'tot'=n) %>% dplyr::select(group, tot) %>%
bind_rows(data.frame('group'='Neuronal', 'tot'=sum(genes_info$Neuronal)),
data.frame('group' = 'Others', 'tot' = sum(genes_info$Group == 'Others')),
data.frame('group'='All', 'tot'=nrow(genes_info)))
lfc_counts_all = lfc_counts_all %>% filter(lfc!=-1) %>% #, group!='Others') %>%
left_join(tot_counts, by='group') %>% mutate('perc'=round(100*as.numeric(n)/tot,2))
# Plot change of number of genes
ggplotly(lfc_counts_all %>% filter(group != 'All') %>%
mutate(group = factor(group, levels = c('SFARI', 'Neuronal', 'Others'))) %>%
ggplot(aes(lfc, perc, color=group)) + geom_point(aes(id=n)) + geom_line() +
scale_color_manual(values=c('#00A4F7', SFARI_colour_hue(r=c(8,7)))) +
ylab('% of Differentially Expressed Genes') + xlab('Fold Change') +
ggtitle('Effect of filtering thresholds in SFARI Genes') + theme_minimal())Grouping Genes by SFARI Gene Score
Gene Expression
Normalised data
The higher the SFARI score, the higher the mean expression of the gene: This pattern is quite strong and it doesn’t have any biological interpretation, so it’s probably bias in the SFARI score assignment
The higher the SFARI score, the lower the standard deviation: This pattern is not as strong, but it is weird because the data was originally heteroscedastic with a positive relation between mean and variance, so the fact that the relation now seems to have reversed could mean that the vst normalisation ended up affecting the highly expressed genes more than it should have when trying to correct their higher variance
plot_data = data.frame('ID'=rownames(datExpr), 'MeanExpr'=rowMeans(datExpr), 'SDExpr'=apply(datExpr,1,sd)) %>%
left_join(genes_info, by='ID')
comparisons = list(c('1','2'), c('2','3'), c('3','4'), c('4','5'), c('5','6'), c('6','Neuronal'), c('Neuronal','Others'),
c('1','3'), c('3','5'), c('5','Neuronal'),
c('2','4'), c('4','6'), c('6','Others'),
c('1','4'), c('4','Neuronal'),
c('2','5'), c('5','Others'),
c('3','Neuronal'), c('1','5'), c('2','6'), c('3','Neuronal'), c('4','Others'))
increase = 1
base = 15.5
pos_y_comparisons = c(rep(base, 7), rep(base + increase,3), rep(base + 2*increase,3), rep(base + 3*increase, 2),
rep(base + 4*increase, 2), base + 5:9*increase)
p1 = plot_data %>% ggplot(aes(gene.score, MeanExpr, fill=gene.score)) +
geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) +
stat_compare_means(comparisons = comparisons, label = 'p.signif', method = 't.test',
method.args = list(var.equal = FALSE), label.y = pos_y_comparisons, tip.length = .02) +
scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) +
xlab('SFARI Gene Scores') + ylab('Mean Expression') +
theme_minimal() + theme(legend.position='none')
increase = 0.03
base = 0.4
pos_y_comparisons = c(rep(base, 7), rep(base + increase,3), rep(base + 2*increase,3), rep(base + 3*increase, 2),
rep(base + 4*increase, 2), base + 5:9*increase)
p2 = plot_data %>% ggplot(aes(gene.score, SDExpr, fill=gene.score)) +
geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) +
stat_compare_means(comparisons = comparisons, label = 'p.signif', method = 't.test',
method.args = list(var.equal = FALSE), label.y = pos_y_comparisons, tip.length = .005) +
scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) +
coord_cartesian(ylim= c(0.05, max(pos_y_comparisons))) +
xlab('SFARI Gene Scores') + ylab('Standard Deviation') +
theme_minimal() + theme(legend.position='none')
grid.arrange(p1, p2, nrow=1)
rm(p1, p2, base, increase, pos_y_comparisons)Raw data
Just to corroborate that the relation between sd and SFARI score used to be in the opposite direction before the normalisation: The higher the SFARI score the higher the mean expression and the higher the standard deviation
*There are a lot of outliers, but the plot is interactive so you can zoom in
# Save preprocessed results
datExpr_prep = datExpr
datMeta_prep = datMeta
genes_info_prep = genes_info
load('./../Data/filtered_raw_data.RData')
plot_data = data.frame('ID'=rownames(datExpr), 'MeanExpr'=rowMeans(datExpr), 'SDExpr'=apply(datExpr,1,sd)) %>%
left_join(genes_info, by='ID')
p1 = ggplotly(plot_data %>% ggplot(aes(gene.score, MeanExpr, fill=gene.score)) +
geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) +
scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) + theme_minimal() +
theme(legend.position='none'))
p2 = ggplotly(plot_data %>% ggplot(aes(gene.score, SDExpr, fill=gene.score)) +
geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) +
scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) + theme_minimal() +
ggtitle('Mean Expression (left) and SD (right) by SFARI score') +
theme(legend.position='none'))
plotly::subplot(p1, p2, nrows=1)#Return to normalised version of the data
datExpr = datExpr_prep
datMeta = datMeta_prep
genes_info = genes_info_prep
rm(plot_data, p1, p2, datExpr_prep, datMeta_prep, genes_info_prep)Log Fold Change
Log Fold Change Direction
The proportion of over- and under-expressed genes in each SFARI Gene score is not very different to the proportion in the genes iwth Neuronal annotations nor in the rest of the genes (good, something less to worry about)
aux = genes_info %>% dplyr::select(ID, log2FoldChange, gene.score) %>%
left_join(data.frame('ID' = rownames(datExpr), 'meanExpr' = rowMeans(datExpr)), by = 'ID') %>%
dplyr::mutate(direction = ifelse(log2FoldChange>0, 'over-expressed', 'under-expressed'))
plot_data = aux %>% group_by(gene.score, direction) %>% tally(name = 'p') %>%
left_join(aux %>% group_by(gene.score) %>% tally, by = 'gene.score') %>% mutate(p = p/n, y=1)
plot_data %>% ggplot(aes(gene.score, p, fill=direction)) + geom_bar(stat='identity') +
geom_hline(yintercept = mean(plot_data$p[plot_data$direction=='under-expressed']),
linetype = 'dashed', color = 'white') +
ylab('Proportion') + xlab('SFARI Gene Scores') +
ggtitle('Direction of Fold-Change in genes by SFARI Score') + theme_minimal()
rm(aux)Log Fold Change Magnitude
There seems to be a negative relation between SFARI score and log fold change when it would be expected to be either positively correlated or independent from each other (this last one because there are other factors that determine if a gene is releated to Autism apart from differences in gene expression)
Wikipedia mentions the likely explanation for this: “A disadvantage and serious risk of using fold change in this setting is that it is biased and may misclassify differentially expressed genes with large differences (B − A) but small ratios (B/A), leading to poor identification of changes at high expression levels”.
Based on this, since we saw there is a strong relation between SFARI score and mean expression, the bias in log fold change affects mainly genes with high SFARI scores, which would be the ones we are most interested in.
On top of this, I believe this effect is made more extreme by the pattern found in the previous plots, since the higher expressed genes were the most affected by the normalisation transformation, ending up with a smaller variance than the rest of the data, which is related to smaller ratios. (This is a constant problem independently of the normalisation function used).
Note: For clarity, the plot was truncated removing some outlier values
increase = 0.06
base = 0.5
pos_y_comparisons = c(rep(base, 7), rep(base + increase,3), rep(base + 2*increase,3), rep(base + 3*increase, 2),
rep(base + 4*increase, 2), base + 5:9*increase)
genes_info %>% ggplot(aes(gene.score, abs(log2FoldChange), fill=gene.score)) +
geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) +
stat_compare_means(comparisons = comparisons, label = 'p.signif', method = 't.test',
method.args = list(var.equal = FALSE), label.y = pos_y_comparisons, tip.length = .005) +
scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) +
coord_cartesian(ylim = c(0, max(pos_y_comparisons))) +
xlab('SFARI Gene Scores') + ylab('LFC Magnitude') +
theme_minimal() + theme(legend.position='none')
rm(increase, base, pos_y_comparisons)We know that in general there is a negative relation between mean expression and lFC in genes, and we also know that there is a strong relation between SFARI Gene Scores and the mean level of expression of the genes.
This could explain the behaviour we found above, but we want to see if, once you control for the level of expression, the SFARI genes continue to have this relation to LFC or if it dissapears. (Being optimistic, perhaps the SFARI genes actually have higher LFC than genes with similar levels of expression, but we can’t see this in the original plot because of the relation between level of expression and LFC)
plot_data = genes_info %>% dplyr::select(ID, log2FoldChange, gene.score, significant) %>%
left_join(data.frame('ID' = rownames(datExpr), 'meanExpr' = rowMeans(datExpr)), by = 'ID') %>%
mutate(alpha = ifelse(gene.score == 'Others' , 0.1, ifelse(gene.score == 'Neuronal', 0.3, 0.7)))
increase = 1
base = 15.5
pos_y_comparisons = c(rep(base, 7), rep(base + increase,3), rep(base + 2*increase,3), rep(base + 3*increase, 2),
rep(base + 4*increase, 2), base + 5:9*increase)
p1 = plot_data %>% ggplot(aes(gene.score, meanExpr, fill=gene.score)) +
geom_boxplot(outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) +
stat_compare_means(comparisons = comparisons, label = 'p.signif', method = 't.test',
method.args = list(var.equal = FALSE), label.y = pos_y_comparisons, tip.length = .02) +
scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) +
xlab('SFARI Gene Scores') + ylab('Mean Expression') +
theme_minimal() + theme(legend.position='none')
p2 = plot_data %>% ggplot(aes(meanExpr, abs(log2FoldChange), color = gene.score)) +
geom_point(alpha=plot_data$alpha) + geom_smooth(method='lm', color='#999999') +
ylab('LogFoldChange Magnitude') + xlab('Mean Expression') +
scale_color_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) +
theme_minimal() + theme(legend.position = 'none')
p2 = ggExtra::ggMarginal(p2, type='density',groupColour = TRUE, size=10)
grid.arrange(p2, p1, ncol=2, widths = c(0.6, 0.4))
rm(p1, p2)This plot shows that our above hypothesis was incorrect: In general, the higher the level of expression, the lower the LFC Magnitude, but this pattern flattens for the genes with the highest levels of expression of the whole dataset, which is the region where the SFARI Genes are except for the SFARI SCore 6. So based on their neighbourhood by level of expression, we would expect SFARI Genes with score 6 to have higher LFC manitudes and the rest of them to have similar ones (and perhaps slightly higher for SFARI Score 1, but definitely not lower)
plot_data = data.frame('meanExpr' = rowMeans(datExpr), 'LFC_magnitude' = abs(genes_info$log2FoldChange),
'gene.score' = genes_info$gene.score, 'p' = NA) %>% arrange(meanExpr)
w = 1000
for(i in 1:(nrow(plot_data)-w)){
plot_data$p[i+floor(w/2)] = mean(plot_data$LFC_magnitude[i:(i+w)])
}
aux_data = plot_data %>% filter(!gene.score %in% c('Neuronal','Others')) %>% group_by(gene.score) %>%
dplyr::summarise(mean_by_score = mean(meanExpr)) %>% ungroup %>%
mutate('color' = SFARI_colour_hue(r=1:6))
ggplotly(plot_data %>% filter(!is.na(p)) %>% ggplot(aes(meanExpr, p)) + geom_line() +
xlab('Mean Level of Expression') + ylab('Sliding Average of LFC Magnitude') +
geom_vline(data = aux_data, aes(xintercept = mean_by_score), color = aux_data$color) +
ggtitle('Sliding Average of LFC Magnitude by Mean Level of Expression') + theme_minimal())rm(aux_data)Fold-Change Magnitude controlling by level of expression
We want to know what happens to the originally negative relation we found between SFARI Gene scores and lFC magnitude when we control for level of expression.
To do this, I’m going to compare each SFARI Gene with its closest non-SFARI neighbours following these steps:
Select one SFARI gene
Select its neighbours: 100 non-SFARI genes with the most similar mean level of Expression
Standardise the lFC magnitude of each of the neighbours and of the SFARI gene (using the mean and sd of the lFC magnitude of only these 101 genes)
Repeat this for each of the SFARI Genes, saving the standardised lFC magnitudes of all the SFARI genes and all the neighbours
Compare the distribution of this value between these two groups (SFARI and their neighbours)
This plot shows the general idea of steps 1, 2, and 3, selecting a random SFARI gene:
The plot on the left shows the original mean expression and lFC magnitude of the SFARI Gene and its 100 closest neighbours
The plot on the right shows the standardised lFC mangitude of the genes, and the vertical lines represent the value that is going to be recorded for each of this genes to be compared afterwards
n = 100
plot_data = genes_info %>% dplyr::select(ID, log2FoldChange, gene.score) %>%
left_join(data.frame('ID' = rownames(datExpr), 'meanExpr' = rowMeans(datExpr)), by = 'ID')
SFARI_gene = plot_data %>% filter(gene.score %in% c('1','2','3','4','5','6')) %>% sample_n(1) %>%
mutate(d=0, alpha = 1)
nn = plot_data %>% filter(gene.score %in% c('Neuronal','Others')) %>%
mutate(d = abs(meanExpr-SFARI_gene$meanExpr), alpha=0.5) %>% top_n(n=-n, wt = d)
plot_data = rbind(SFARI_gene, nn) %>%
mutate(std_magnitude = (abs(log2FoldChange) - mean(abs(log2FoldChange)))/sd(abs(log2FoldChange)))
p1 = plot_data %>% ggplot(aes(meanExpr, abs(log2FoldChange), color = gene.score)) +
geom_point(alpha = plot_data$alpha) + xlab('Mean Expression') + ylab('Log2 Fold Change Magnitude') +
scale_color_manual(values=SFARI_colour_hue(r=c(as.numeric(SFARI_gene$gene.score),8,7))) +
theme_minimal() + theme(legend.position='none')
p2 = plot_data %>% ggplot(aes(meanExpr, std_magnitude, color = gene.score)) +
geom_point(alpha = plot_data$alpha) +
geom_hline(aes(yintercept = mean(std_magnitude)), linetype = 'dashed', color = '#999999') +
scale_color_manual(values=SFARI_colour_hue(r=c(as.numeric(SFARI_gene$gene.score),8,7))) +
geom_segment(aes(x=SFARI_gene$meanExpr, y=mean(std_magnitude), xend = SFARI_gene$meanExpr,
yend = std_magnitude[1]), alpha = 0.5,
color = SFARI_colour_hue(r=1:8)[as.numeric(SFARI_gene$gene.score)]) +
xlab('Mean Expression') + ylab('Standardised LFC Magnitude') +
theme_minimal() + theme(legend.position='none')
for(i in 1:15){
random_sample = plot_data %>% filter(gene.score != SFARI_gene$gene.score) %>% sample_n(1)
p2 = p2 + geom_segment(x=random_sample$meanExpr, xend = random_sample$meanExpr, y=mean(plot_data$std_magnitude),
yend = random_sample$std_magnitude, alpha = 0.5, color = 'gray')
}
grid.arrange(p1, p2, ncol=2, top='Comparing SFARI Genes with their n closest neighbours by Mean Expression')
cat(paste0('SFARI gene\'s standardised distance to its neigbours\'s LFC magnitude: ',
round(plot_data$std_magnitude[1],4)))## SFARI gene's standardised distance to its neigbours's LFC magnitude: 1.737rm(p1, p2, SFARI_gene, nn, random_sample, i)As steps 4, and 5, say, we repeat this for all of the SFARI Genes, recording their standardised mangnitude as well as the ones from their neighbours so we can study them all together
Results
Even when controlling for the relation between Mean Expression and LFC by comparing each SFARI Gene only with neighbouring genes, we see the same results as before!
Neuronal genes have higher magnitudes of lFC than non-SFARI, non-neuronal genes consistently (makes sense)
The higher the SFARI Gene score, the lower the LFC (even with genes with the same level of expression!)
The difference with the Neuronal group is statistically significant for all SFARI Scores except scores 5 and 6
get_std_lfc_magnitudes = function(data_info, SFARI_score, n){
SFARI_genes = data_info %>% filter(gene.score == as.character(SFARI_score))
std_magnitudes = data.frame(gene.score = as.character(), std_magnitude = as.numeric)
for(i in 1:nrow(SFARI_genes)){
SFARI_gene = SFARI_genes[i,]
nn = data_info %>% filter(gene.score %in% c('Neuronal','Others')) %>%
mutate(d = abs(meanExpr-SFARI_gene$meanExpr)) %>% top_n(n=-n, wt = d) %>% dplyr::select(-d)
iter_data = rbind(SFARI_gene, nn) %>%
mutate(std_magnitude = (abs(log2FoldChange) - mean(abs(log2FoldChange)))/sd(abs(log2FoldChange))) %>%
dplyr::select(gene.score, std_magnitude)
std_magnitudes = rbind(std_magnitudes, iter_data)
}
return(std_magnitudes)
}
create_plot_by_SFARI_score = function(score, n) {
std_magnitudes = get_std_lfc_magnitudes(data_info, score, n)
plot = std_magnitudes %>% ggplot(aes(gene.score, std_magnitude)) +
geom_boxplot(aes(fill = gene.score), outlier.colour='#cccccc', outlier.shape='o', outlier.size=3) +
xlab('') + ylab('Standardised LFC Magnitude') +
scale_fill_manual(values=SFARI_colour_hue(r=c(score,8,7))) +
coord_cartesian(ylim = c(min(std_magnitudes$std_magnitude), 3)) +
stat_compare_means(method = 't.test', method.args = list(var.equal = FALSE), label = 'p.signif',
ref.group = as.character(score), label.y = 3) +
theme_minimal() + theme(legend.position = 'none')
return(plot)
}
data_info = genes_info %>% dplyr::select(ID, log2FoldChange, gene.score) %>%
left_join(data.frame('ID' = rownames(datExpr), 'meanExpr' = rowMeans(datExpr)), by = 'ID')
p1 = create_plot_by_SFARI_score(1,n)
p2 = create_plot_by_SFARI_score(2,n)
p3 = create_plot_by_SFARI_score(3,n)
p4 = create_plot_by_SFARI_score(4,n)
p5 = create_plot_by_SFARI_score(5,n)
p6 = create_plot_by_SFARI_score(6,n)
grid.arrange(p1, p2, p3, p4, p5, p6, nrow=2,
top = 'Comparison of LFC Magnitude of SFARI gens and their closest neighbours by Mean Expression')
rm(p1, p2, p3, p4, p5, p6, get_std_lfc_magnitudes, create_plot_by_SFARI_score)Differential Expression
The proportion of DE genes for each SFARI Genes is quite similar, but it tends to be lower for the highest scores
plot_info = genes_info %>% group_by(gene.score, significant) %>% tally(name = 'DE') %>% ungroup %>% ungroup %>%
left_join(genes_info %>% group_by(gene.score) %>% tally(name = 'total') %>%
ungroup, by = 'gene.score') %>% filter(significant) %>%
mutate('perc' = 100*DE/total)
ggplotly(plot_info %>% ggplot(aes(gene.score, perc, fill = gene.score)) + geom_bar(stat='identity') +
xlab('SFARI Gene Score') + ylab('% of DE genes') + theme_minimal() + theme(legend.position = 'none') +
scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))))But in our dataset, the higher the level of expression of a gene, the more likely the gene is to be DE (this can be seen by ordering the genes by level of expression and calculating the proportion of DE Genes using a sliding window). Based one this, the SFARI Score 1 should have the highest proportion of DE Genes, followed by the others and SFARI Score 6 should have the lowest proportion of all.
plot_data = data.frame('meanExpr' = rowMeans(datExpr), 'DE' = genes_info$significant,
'gene.score' = genes_info$gene.score, 'p' = NA) %>% arrange(meanExpr)
w = 1000
for(i in 1:(nrow(plot_data)-w)){
plot_data$p[i+floor(w/2)] = mean(plot_data$DE[i:(i+w)])*100
}
aux_data = plot_data %>% filter(!gene.score %in% c('Neuronal','Others')) %>% group_by(gene.score) %>%
dplyr::summarise(mean_by_score = mean(meanExpr)) %>% ungroup %>%
mutate('color' = SFARI_colour_hue(r=1:6))
ggplotly(plot_data %>% filter(!is.na(p)) %>% ggplot(aes(meanExpr, p)) + geom_line() +
xlab('Mean Level of Expression') + ylab('Sliding Percentage of DE Genes') +
geom_vline(data = aux_data, aes(xintercept = mean_by_score), color = aux_data$color) +
ggtitle('Sliding Percentage of DE Genes by Mean Level of Expression') + theme_minimal()) rm(aux_data)Differential Expression controlling by level of expression
We want to see how the different scores in the SFARI Genes compare to other groups of genes with similar levels of expression when studying the proportion of DE genes
To do this, I’m going to compare each SFARI Gene with its closest non-SFARI neighbours following these steps:
Select one SFARI gene
Select its neighbours: 100 non-SFARI genes with the most similar mean level of Expression
Calculate the % of these neighbours that are DE and store this value
Repeat this for all of the genes in a specific SFARI score: We have a distribution of % DE neighbours and a single value indicating the percentage of DE genes in that SFARI score
4.1 Measure how annomalous the value for the SFARI scores is by calculating its distance to the distribution (in standard devitions)
- Repeat this for the other SFARI Gene scores
Notes:
The higher the SFARI Score, the farther away its percentage of DE genes is from the distribution of its neighbours’ DE Genes, both for Neuronal and Others groups
get_neighbours_DE = function(data_info, SFARI_score, n){
SFARI_genes = data_info %>% filter(gene.score == as.character(SFARI_score))
perc_DE = data.frame(gene.score = as.character(), p_DE = as.numeric)
for(i in 1:nrow(SFARI_genes)){
SFARI_gene = SFARI_genes[i,]
nn = data_info %>% filter(gene.score %in% c('Neuronal','Others')) %>%
mutate(d = abs(meanExpr-SFARI_gene$meanExpr)) %>% top_n(n=-n, wt = d) %>%
group_by(gene.score) %>% summarise(perc_DE = 100*mean(significant)) %>% ungroup
perc_DE = rbind(perc_DE, nn)
}
colnames(perc_DE) = c('gene.score', 'perc_DE')
return(perc_DE)
}
calc_dist = function(SFARI_score, df, group){
SFARI_p = 100*mean(genes_info$significant[genes_info$gene.score==SFARI_score])
mean_nn = df$perc_DE[df$gene.score == group] %>% mean
sd_nn = df$perc_DE[df$gene.score == group] %>% sd
dist = round(abs(SFARI_p-mean_nn)/sd_nn, 2)
return(dist)
}
create_plot_by_SFARI_score = function(score, n) {
perc_DE_nn = get_neighbours_DE(data_info, score, n)
plot = perc_DE_nn %>% ggplot(aes(gene.score, perc_DE, fill = gene.score)) + geom_boxplot() +
xlab('') + ylab('% of DE Genes') +
geom_hline(yintercept = 100*mean(genes_info$significant[genes_info$gene.score==as.character(score)]),
color = SFARI_colour_hue(r=1:6)[score]) +
ggtitle(paste0('Neighbours of SFARI Score 1 Genes',
'\n\n Dist to Neuronal: ',calc_dist(as.character(score),perc_DE_nn,'Neuronal'),' SD',
'\n Dist to Others: ', calc_dist(as.character(score), perc_DE_nn, 'Others'),' SD')) +
scale_fill_manual(values=SFARI_colour_hue(r=c(8,7))) + theme_minimal() + theme(legend.position='none')
return(plot)
}
data_info = genes_info %>% dplyr::select(ID, significant, gene.score) %>%
left_join(data.frame('ID' = rownames(datExpr), 'meanExpr' = rowMeans(datExpr)), by = 'ID')
n = 100
p1 = create_plot_by_SFARI_score(1, n)
p2 = create_plot_by_SFARI_score(2, n)
p3 = create_plot_by_SFARI_score(3, n)
p4 = create_plot_by_SFARI_score(4, n)
p5 = create_plot_by_SFARI_score(5, n)
p6 = create_plot_by_SFARI_score(6, n)
grid.arrange(p1, p2, p3, p4, p5, p6, nrow = 2)
rm(p1, p2, p3, p4, p5, p6, get_neighbours_DE, calc_dist, create_plot_by_SFARI_score)Effects of modifying filtering threshold by SFARI score
The higher the SFARI Score, the lower the % of DE Genes it contains
All SFARI scores except score 6 are more affected by the filtering than the genes with Neuronal annotations
Using the null hypothesis \(H_0: lfc=0\), 272/902 SFARI genes are statistically significant (~30%)
lfc_list = seq(1, 1.2, 0.01)
all_counts = data.frame('group'='All', 'n'=as.character(nrow(genes_info)))
Others_counts = data.frame('group'='Others', n=as.character(sum(genes_info$gene.score == 'Others')))
Neuronal_counts = data.frame('group'='Neuronal', n=as.character(sum(genes_info$Neuronal)))
lfc_counts_all = genes_info %>% group_by(`gene-score`) %>% filter(`gene-score` != 'Others') %>% tally %>%
mutate('group'=as.factor(`gene-score`), 'n'=as.character(n)) %>%
dplyr::select(group, n) %>%
bind_rows(Neuronal_counts, Others_counts, all_counts) %>%
mutate('lfc'=-1) %>% dplyr::select(lfc, group, n)
for(lfc in lfc_list){
# Recalculate genes_info with the new threshold (p-values change)
DE_genes = results(dds, lfcThreshold=log2(lfc), altHypothesis='greaterAbs') %>% data.frame
DE_genes = DE_genes %>% mutate('ID'=rownames(.)) %>% left_join(SFARI_genes, by='ID') %>%
mutate(`gene-score`=ifelse(is.na(`gene-score`), 'Others', `gene-score`)) %>%
distinct(ID, .keep_all = TRUE) %>% left_join(GO_neuronal, by='ID') %>%
mutate(Neuronal=ifelse(is.na(Neuronal), 0, Neuronal)) %>%
mutate(gene.score=ifelse(`gene-score`=='Others' & Neuronal==1, 'Neuronal', `gene-score`))
DE_genes = DE_genes %>% filter(padj<0.05 & abs(log2FoldChange)>log2(lfc))
# Calculate counts by groups
all_counts = data.frame('group'='All', 'n'=as.character(nrow(DE_genes)))
Others_counts = data.frame('group'='Others', n=as.character(sum(DE_genes$`gene-score` == 'Others')))
Neuronal_counts = data.frame('group'='Neuronal', n=as.character(sum(DE_genes$Neuronal)))
lfc_counts = DE_genes %>% group_by(`gene-score`) %>% tally %>%
mutate('group'=`gene-score`, 'n'=as.character(n)) %>%
bind_rows(Neuronal_counts, all_counts) %>%
mutate('lfc'=lfc) %>% dplyr::select(lfc, group, n)
# Update lfc_counts_all
lfc_counts_all = lfc_counts_all %>% bind_rows(lfc_counts)
}
# Add missing entries with 0s
lfc_counts_all = expand.grid('group'=unique(lfc_counts_all$group), 'lfc'=unique(lfc_counts_all$lfc)) %>%
left_join(lfc_counts_all, by=c('group','lfc')) %>% replace(is.na(.), 0)
# Calculate percentage of each group remaining
tot_counts = genes_info %>% group_by(`gene-score`) %>% tally() %>% filter(`gene-score`!='Others') %>%
mutate('group'=`gene-score`, 'tot'=n) %>% dplyr::select(group, tot) %>%
bind_rows(data.frame('group'='Neuronal', 'tot'=sum(genes_info$Neuronal)),
data.frame('group'='Others', 'tot'=sum(genes_info$gene.score=='Others'&!genes_info$Neuronal)),
data.frame('group'='All', 'tot'=nrow(genes_info)))
lfc_counts_all = lfc_counts_all %>% filter(lfc!=-1) %>% #, group!='Others') %>%
left_join(tot_counts, by='group') %>% mutate('perc'=round(100*as.numeric(n)/tot,2))
# Plot change of number of genes
ggplotly(lfc_counts_all %>% filter(group != 'All') %>% ggplot(aes(lfc, perc, color=group)) +
geom_point(aes(id=n)) + geom_line() + scale_color_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) +
ylab('% of Differentially Expressed Genes') + xlab('Fold Change') +
ggtitle('Effect of filtering thresholds by SFARI score') + theme_minimal())rm(lfc_list, all_counts, Neuronal_counts, lfc_counts_all, lfc, lfc_counts, lfc_counts_all, tot_counts,
lfc_counts_all, Others_counts)Session info
sessionInfo()## R version 3.6.3 (2020-02-29)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.4 LTS
##
## Matrix products: default
## BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.7.1
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.7.1
##
## locale:
## [1] LC_CTYPE=en_GB.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_GB.UTF-8 LC_COLLATE=en_GB.UTF-8
## [5] LC_MONETARY=en_GB.UTF-8 LC_MESSAGES=en_GB.UTF-8
## [7] LC_PAPER=en_GB.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] parallel stats4 stats graphics grDevices utils datasets
## [8] methods base
##
## other attached packages:
## [1] kableExtra_1.1.0 knitr_1.28
## [3] expss_0.10.2 DESeq2_1.24.0
## [5] SummarizedExperiment_1.14.1 DelayedArray_0.10.0
## [7] BiocParallel_1.18.1 matrixStats_0.56.0
## [9] Biobase_2.44.0 GenomicRanges_1.36.1
## [11] GenomeInfoDb_1.20.0 IRanges_2.18.3
## [13] S4Vectors_0.22.1 BiocGenerics_0.30.0
## [15] ClusterR_1.2.1 gtools_3.8.2
## [17] Rtsne_0.15 ggpubr_0.2.5
## [19] magrittr_1.5 GGally_1.5.0
## [21] gridExtra_2.3 viridis_0.5.1
## [23] viridisLite_0.3.0 RColorBrewer_1.1-2
## [25] plotlyutils_0.0.0.9000 plotly_4.9.2
## [27] glue_1.4.1 reshape2_1.4.4
## [29] forcats_0.5.0 stringr_1.4.0
## [31] dplyr_1.0.0 purrr_0.3.4
## [33] readr_1.3.1 tidyr_1.1.0
## [35] tibble_3.0.1 ggplot2_3.3.2
## [37] tidyverse_1.3.0
##
## loaded via a namespace (and not attached):
## [1] readxl_1.3.1 backports_1.1.8 Hmisc_4.4-0
## [4] plyr_1.8.6 lazyeval_0.2.2 splines_3.6.3
## [7] gmp_0.5-13.6 crosstalk_1.1.0.1 digest_0.6.25
## [10] htmltools_0.4.0 fansi_0.4.1 checkmate_2.0.0
## [13] memoise_1.1.0 cluster_2.1.0 annotate_1.62.0
## [16] modelr_0.1.6 jpeg_0.1-8.1 colorspace_1.4-1
## [19] blob_1.2.1 rvest_0.3.5 haven_2.2.0
## [22] xfun_0.12 crayon_1.3.4 RCurl_1.98-1.2
## [25] jsonlite_1.7.0 genefilter_1.66.0 survival_3.1-12
## [28] gtable_0.3.0 zlibbioc_1.30.0 XVector_0.24.0
## [31] webshot_0.5.2 scales_1.1.1 DBI_1.1.0
## [34] miniUI_0.1.1.1 Rcpp_1.0.4.6 xtable_1.8-4
## [37] htmlTable_1.13.3 foreign_0.8-76 bit_1.1-15.2
## [40] Formula_1.2-3 htmlwidgets_1.5.1 httr_1.4.1
## [43] acepack_1.4.1 ellipsis_0.3.1 pkgconfig_2.0.3
## [46] reshape_0.8.8 XML_3.99-0.3 farver_2.0.3
## [49] nnet_7.3-14 dbplyr_1.4.2 locfit_1.5-9.4
## [52] later_1.0.0 tidyselect_1.1.0 labeling_0.3
## [55] rlang_0.4.6 AnnotationDbi_1.46.1 munsell_0.5.0
## [58] cellranger_1.1.0 tools_3.6.3 cli_2.0.2
## [61] generics_0.0.2 RSQLite_2.2.0 broom_0.5.5
## [64] fastmap_1.0.1 evaluate_0.14 yaml_2.2.1
## [67] bit64_0.9-7 fs_1.4.0 nlme_3.1-147
## [70] mime_0.9 ggExtra_0.9 xml2_1.2.5
## [73] compiler_3.6.3 rstudioapi_0.11 png_0.1-7
## [76] ggsignif_0.6.0 reprex_0.3.0 geneplotter_1.62.0
## [79] stringi_1.4.6 highr_0.8 lattice_0.20-41
## [82] Matrix_1.2-18 vctrs_0.3.1 pillar_1.4.4
## [85] lifecycle_0.2.0 data.table_1.12.8 bitops_1.0-6
## [88] httpuv_1.5.2 R6_2.4.1 latticeExtra_0.6-29
## [91] promises_1.1.0 assertthat_0.2.1 withr_2.2.0
## [94] GenomeInfoDbData_1.2.1 mgcv_1.8-31 hms_0.5.3
## [97] grid_3.6.3 rpart_4.1-15 rmarkdown_2.1
## [100] shiny_1.4.0.2 lubridate_1.7.4 base64enc_0.1-3